Not content to wait five days for the humanitarian visas Mexico is offering them, several hundred migrants took to make-shift rafts to cross the Suchiate River, which forms the frontier, or snuck across the loosely guarded border bridge overnight, AFP correspondents said.
Their advance could trigger a new Twitter firestorm from US President Donald Trump, who has urged Mexico to halt such caravans, and who tweeted early Friday: "Another big Caravan heading our way. Very hard to stop without a Wall!" Hundreds more of the 2,000 migrants in the caravan gathered patiently on the border bridge, trickling into Mexico as the authorities processed them.
The authorities will set up checkpoints in southern Mexico to make migrants who snuck into the country register for visas, said Alejandro Encinas, under-secretary for migration.
"We are informing all of them that they must comply with our country's laws," he said.
Caravans of migrants seeking safety in numbers have taken center stage in the raging debate in the United States over Trump's proposed border wall, which has led to a government shutdown that is now the longest in history.
The latest caravan is smaller than the one that swelled to 7,000 migrants late last year, leading Trump to warn of an "invasion" by "hardened criminals" and send thousands of troops to the US-Mexican border.
Mexican authorities are urging the migrants to arrive legally and offering expedited "visitor cards" that let them work and access basic health care in Mexico.
So far, 969 migrants from Honduras, El Salvador, Guatemala and Nicaragua have registered under the program, receiving bracelets that they can exchange for visitor cards in five days.
But hundreds more ignored the offer.
"A lot of us aren't interested in waiting five days. Our goal is to reach the United States," said Alma Mendoza, a nurse and single mother making the trip with her three children.
"We don't have food, much less money. We want to reach our destination," she told AFP.
Other migrants said they would consider staying in Mexico.
"My goal is to reach the United States, but if I can't I'll stay in Mexico and work. They're giving us an opportunity," said Christian Medrano, 33, an industrial technician.
Mexico meanwhile announced a fresh policy under which Central Americans fleeing poverty and violence with the intention of reaching the United States may remain in Mexico for a year.
The decision "recognizes the importance of our relationship with Central America," especially El Salvador, Guatemala and Honduras, said Tonatiuh Guillen, commissioner of the Mexican National Institute of Migration.
The caravan set out Tuesday from San Pedro Sula, in northwestern Honduras, and has grown along the way.
The migrants are mostly fleeing poverty and crime in Central America's "Northern Triangle" of El Salvador, Guatemala and Honduras. Brutal street gangs have made the three countries among the most violent in the world.
Another caravan of about 200 migrants set out Wednesday from El Salvador and is now in southern Mexico, possibly poised to join up with the first.
Many of the migrants are travelling in families, often with small children.
They have covered about 700 kilometers (435 miles) so far, and have roughly 4,000 kms to go if they take the same route as the last caravan, to Tijuana, across from San Diego, California.
When that caravan reached Mexico in October, the authorities tried to stop it with riot police. But the migrants stormed in anyway, tearing down border fences and crossing the river illegally when police refused to let them through.
Since then, Mexico has gotten a new government, led by President Andres Manuel Lopez Obrador, an anti-establishment leftist.
"AMLO," as the new president is widely known, has promised to treat migrants more humanely than previous administrations. But he has also sought to stay on Trump's good side with talk of reducing migrant flows.
The October caravan largely dispersed after reaching Tijuana. US Border Patrol agents fought back two attempts by the migrants to rush the border, firing tear gas to disperse them.
Some have since found work in Mexico, some crossed the border and filed asylum claims, and many returned home. About 400 remain in a shelter set up for them in Tijuana that is slated to be closed on Wednesday.